Math @ Duke

Publications [#150242] of Mark Huber
Papers Submitted
 M. L. Huber and R. L. Wolpert, Perfect Simulation of Matern Type III Repulsive Point Processes
(September, 2008)
(last updated on 2008/10/06)
Abstract: In a repulsive point process, points act as if they are repelling one another, leading to configurations that are overdispersed when compared to a standard Poisson point process. These models are useful wherever competition for resources exists, such as in the locations of towns and trees. Bertil Matern introduced three approaches to modeling repulsive point processes but described only two in detail, now called the Matern processes of Types I and II; the third he regarded as overly complex. In fact it is only this third process, which we call Matern Type III, which has a tractable likelihood function. In this paper a perfect simulation method is developed that allows for arbitrarily accurate approximation of the likelihood for data modeled by the Matern Type III, thereby enabling its use for inference. This method is shown to be fast in practice, generating samples in time that grows nearly linearly in the intensity parameter of the model, while the running times for more naive methods grow exponentially.


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